/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 55 $$-3 x=9$$... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Problem 55

$$-3 x=9$$

Short Answer

Expert verified
x = -3

Step by step solution

01

Identify the equation

The given equation is \[ -3x = 9 \]
02

Isolate the variable

To solve for \( x \), divide both sides of the equation by \( -3 \). \[ -3x \div -3 = \frac{9}{-3} \]
03

Simplify the equation

After dividing, simplify the right side of the equation: \[ x = -3 \]

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Isolating the Variable
The first step in solving linear equations is to isolate the variable you are solving for. In the exercise, the variable is \( x \). Isolating the variable means getting \( x \) alone on one side of the equation, which helps in simplifying our task of finding its value.
For the equation \( -3x = 9 \), we see that \( x \) is currently attached to \(-3\). To isolate \( x \), we need to perform operations that will move everything else to the other side of the equation, leaving \( x \) by itself.
Simplification
Once the variable is isolated, the next major step is simplification. Here, simplifying means making the equation easier to understand and solve.
In our given problem, to isolate \( x \), we divide both sides by \( -3 \):
  • Left side: \( -3x \div -3 \)
  • Right side: \( \frac{9}{-3} \)
This operation cancels out \( -3 \) on the left, leaving us with \( x \).
On the right side, \( 9 \div -3 = -3 \). So, the simplified equation is \( x = -3 \). This simplification step ensures that the equation becomes straightforward and the variable is easily identifiable.
Division in Equations
Division is a key operation in solving many linear equations, as it helps in isolating the variable.
Specifically for our exercise, the division performed was crucial:
  • We divided both sides of the equation by the coefficient of \( x \), which was \( -3 \).
This division helps cancel out the multiplier on the variable side:
  • \( -3x \div -3 \rightarrow x \)
This left us with the simplified form \( x = -3 \).
Remember, whatever operation you do to one side of the equation, you must do to the other. This keeps the equation balanced and leads to the correct solution.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The table represents the world's major consumers of primary energy for a recent year. All measurements are in quadrillions of Btu. Note: 1 quadrillion = 1,000,000,000,000,000. (Source: Energy Information Administration, U.S. Department of Energy) Construct a bar graph using horizontal bars. The length of each bar gives the amount of energy consumed for that country. $$\begin{array}{l|c} \hline \text { Country } & \begin{array}{c} \text { Amount of Energy Consumed } \\ \text { (Quadrillions of Btu) } \end{array} \\ \hline \text { Germany } & 14 \\ \hline \text { Japan } & 22 \\ \hline \text { Russia } & 28 \\ \hline \text { China } & 37 \\ \hline \text { United States } & 99 \\ \hline \end{array}$$ (Bar graph can't copy)

$$y=-3$$

If a die is rolled, in how many ways can an odd number come up?

For Exercises \(29-34\), plot the points on the rectangular coordinate system. $$(-4,0)$$

A coin is tossed twice. Determine the sample space of this experiment.
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.